Known folding mandrels for manufacturing glued sleeves for the manufacture of paper cups have a conical form onto which a plane paper segment is wound. Before winding on of the paper segment, adhesive is applied is an area in which an overlap is to be provided. After being wound onto the folding mandrel, the segment is compressed in the area of the overlap and the segment is connected to form a conical sleeve. To save paper, the overlap is selected as small as possible, and it can then not be completely ruled out that adhesive escapes from the overlap. If adhesive escapes on that side of the overlap facing the folding mandrel, this causes fouling of the folding mandrel surface. This can lead to sticking of the sleeves and to disruptions in the production sequence. To eliminate and prevent such disruptions, the folding mandrel must be cleaned regularly. If adhesive escapes on the other side of the overlap, this escaped adhesive is on the outside of the finished cup. If several cups are then stacked inside one another after completion, this can lead to the stacked cups sticking together.